Computer Sciences Dept.

On the Convolution of a Box Spline with a Compactly Supported Distribution: The Exponential-Polynomials in the Linear Span

Amos Ron and Charles K Chui

The problem of linear independence of the integer translates of where  is a compactly supported distribution and  is an exponential box spline, is considered in this paper. The main result relates the linear independence issue with the distribution of the zeros of the Fourier-Laplace transform  of  on certain linear manifolds associated with . The proof of our result makes an essential use of the necessary and sufficient condition derived in [11]. Several applications to specific situations are discussed. Particularly, it is shown that if the support of  is small enough then linear independence is guaranteed provided that  does not vanish at a certain finite set of critical points associated with . Also, the results here provoke a new proof of the linear independence condition for the translates of  itself.

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